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<div class="subTitle">org.apache.commons.math3.special</div>
<h2 title="Class BesselJ" class="title">Class BesselJ</h2>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></dd>
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<pre>public class <span class="strong">BesselJ</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></pre>
<div class="block">This class provides computation methods related to Bessel
 functions of the first kind. Detailed descriptions of these functions are
 available in <a
 href="http://en.wikipedia.org/wiki/Bessel_function">Wikipedia</a>, <a
 href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">Abrabowitz and
 Stegun</a> (Ch. 9-11), and <a href="http://dlmf.nist.gov/">DLMF</a> (Ch. 10).
 <p>
 This implementation is based on the rjbesl Fortran routine at
 <a href="http://www.netlib.org/specfun/rjbesl">Netlib</a>.</p>
 <p>
 From the Fortran code: </p>
 <p>
 This program is based on a program written by David J. Sookne (2) that
 computes values of the Bessel functions J or I of real argument and integer
 order. Modifications include the restriction of the computation to the J
 Bessel function of non-negative real argument, the extension of the
 computation to arbitrary positive order, and the elimination of most
 underflow.</p>
 <p>
 References:</p>
 <ul>
 <li>"A Note on Backward Recurrence Algorithms," Olver, F. W. J., and Sookne,
 D. J., Math. Comp. 26, 1972, pp 941-947.</li>
 <li>"Bessel Functions of Real Argument and Integer Order," Sookne, D. J., NBS
 Jour. of Res. B. 77B, 1973, pp 125-132.</li>
 </ul> </p></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.4</dd></dl>
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<td class="colFirst"><code>static class&nbsp;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/BesselJ.BesselJResult.html" title="class in org.apache.commons.math3.special">BesselJ.BesselJResult</a></strong></code>
<div class="block">Encapsulates the results returned by <a href="../../../../../org/apache/commons/math3/special/BesselJ.html#rjBesl(double,%20double,%20int)"><code>rjBesl(double, double, int)</code></a>.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/special/BesselJ.html#BesselJ(double)">BesselJ</a></strong>(double&nbsp;order)</code>
<div class="block">Create a new BesselJ with the given order.</div>
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<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/special/BesselJ.BesselJResult.html" title="class in org.apache.commons.math3.special">BesselJ.BesselJResult</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/BesselJ.html#rjBesl(double,%20double,%20int)">rjBesl</a></strong>(double&nbsp;x,
      double&nbsp;alpha,
      int&nbsp;nb)</code>
<div class="block">Calculates Bessel functions \(J_{n+alpha}(x)\) for
 non-negative argument x, and non-negative order n + alpha.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/BesselJ.html#value(double)">value</a></strong>(double&nbsp;x)</code>
<div class="block">Returns the value of the constructed Bessel function of the first kind,
 for the passed argument.</div>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/BesselJ.html#value(double,%20double)">value</a></strong>(double&nbsp;order,
     double&nbsp;x)</code>
<div class="block">Returns the first Bessel function, \(J_{order}(x)\).</div>
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<pre>public&nbsp;BesselJ(double&nbsp;order)</pre>
<div class="block">Create a new BesselJ with the given order.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>order</code> - order of the function computed when using <a href="../../../../../org/apache/commons/math3/special/BesselJ.html#value(double)"><code>value(double)</code></a>.</dd></dl>
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<h4>value</h4>
<pre>public&nbsp;double&nbsp;value(double&nbsp;x)
             throws <a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a>,
                    <a href="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></pre>
<div class="block">Returns the value of the constructed Bessel function of the first kind,
 for the passed argument.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html#value(double)">value</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Argument</dd>
<dt><span class="strong">Returns:</span></dt><dd>Value of the Bessel function at x</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if <code>x</code> is too large relative to <code>order</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></code> - if the algorithm fails to converge</dd></dl>
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<pre>public static&nbsp;double&nbsp;value(double&nbsp;order,
           double&nbsp;x)
                    throws <a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a>,
                           <a href="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></pre>
<div class="block">Returns the first Bessel function, \(J_{order}(x)\).</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>order</code> - Order of the Bessel function</dd><dd><code>x</code> - Argument</dd>
<dt><span class="strong">Returns:</span></dt><dd>Value of the Bessel function of the first kind, \(J_{order}(x)\)</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if <code>x</code> is too large relative to <code>order</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></code> - if the algorithm fails to converge</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/special/BesselJ.BesselJResult.html" title="class in org.apache.commons.math3.special">BesselJ.BesselJResult</a>&nbsp;rjBesl(double&nbsp;x,
                           double&nbsp;alpha,
                           int&nbsp;nb)</pre>
<div class="block">Calculates Bessel functions \(J_{n+alpha}(x)\) for
 non-negative argument x, and non-negative order n + alpha.
 <p>
 Before using the output vector, the user should check that
 nVals = nb, i.e., all orders have been calculated to the desired accuracy.
 See BesselResult class javadoc for details on return values.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - non-negative real argument for which J's are to be calculated</dd><dd><code>alpha</code> - fractional part of order for which J's or exponentially
 scaled J's (\(J\cdot e^{x}\)) are to be calculated. 0 <= alpha < 1.0.</dd><dd><code>nb</code> - integer number of functions to be calculated, nb > 0. The first
 function calculated is of order alpha, and the last is of order
 nb - 1 + alpha.</dd>
<dt><span class="strong">Returns:</span></dt><dd>BesselJResult a vector of the functions
 \(J_{alpha}(x)\) through \(J_{nb-1+alpha}(x)\), or the corresponding exponentially
 scaled functions and an integer output variable indicating possible errors</dd></dl>
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